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11  Superposition Method with the Principle of Multiple Shooting for Solving Stiff Linear Initial Value Problems Basheer M.S. Khalaf Suhaib A. Al-Tamr College of Education University of Mosul, Iraq Received on: 10/08/2002 Accepted on: 04/01/2003 Abstract The main objective of this paper is the development of a new technique for solving stiff Linear Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs), The new Technique consists of combining the linear superposition principle with the principle of Multiple shooting. We have applied the new technique successfully for solving hard stiff IVPs. Also we have studied the ability of the new technique for controlling the stability of the numerical solution of IVPs and how the new technique prevents the accumulation of round off errors.